Two balls roll toward each other.
The red ball has a mass of 0.5 kg and a speed of 4 m/s just before
impact. The green ball has a mass of 0.3 kg and a speed of 2 m/s.
After the head on collision, the red ball continues forward with
a speed of 2 m/s. Find the speed of the green ball after the collision.
Was the collision elastic?

A steel ball of mass m is fastened
to a light cord of length L and released when the cord is horizontal.
At the bottom of its path, the ball strikes a hard plastic block
of mass M = 4m, initially at rest on a frictionless surface. The
collision is elastic.

(a) Find the tension in the cord
when the ball's height above its lowest position is 0.5L. Write your
answer in terms of m and g.

(b) Find the speed of the block
immediately after the collision.

(c) To what height h will the
ball rebound after the collision?

Solution

Problem 7-30

A ballistic pendulum is a device
that may be used to measure the muzzle speed of a bullet. It is
composed of a wooden block suspended from a horizontal support by
cords attached at each end. A bullet is shot into the block, and
as a result of the perfectly inelastic impact, the block swings upward.
Consider a bullet (mass m) with velocity v as it enters the block
(mass M). The length of the cords supporting the block each have
length L. The maximum height to which the block swings upward after
impact is denoted by y, and the maximum horizontal displacement
is denoted by x.

(a) In terms of m, M, g, and
y, determine the speed v of the bullet.

(b) What fraction of the bullet's
original kinetic energy is lost as a result of the collision? What
happens to the lost kinetic energy?

(c) If y is very small (so that can
be neglected), determine the speed of the bullet in terms of m, M,
g, x, and L.

(d) Once the block begins to
swing, does the momentum of the block remain constant? Why or why
not?

Solution

Problem 7-31

An object of mass m moves with
velocity v toward a stationary object of the same mass. After their
impact, the objects move off in the directions shown in the following
diagram:

(a) If denotes
the kinetic energy of Object 1 before collision, what is the kinetic
energy of this object after collision? Write your answer in terms
of and .

(b) What is the kinetic energy
of Object 2 after the collision? Write your answer in terms of and .